I use “bounce” all the time in the context of cycling something– “Bouncing a service”, “Bouncing a server”, “Bouncing a router”, etc. I’d use it interchangeably with “restart”, “reboot”, or “power cycle”.
It seems to be slightly regional, being most popular in the Midwest, Northeast, and West coast. The term seems to have originated in the IBM, VAX, and Unix communities; as according to the Jargon File. It seems rare for people to use the term outside of these regions.
I wouldn’t say it’s in extremely common use, but it’s out there.